Solve for $x$ : $x^2 - 12x + 32 = 0$
Answer: The coefficient on the $x$ term is $-12$ and the constant term is $32$ , so we need to find two numbers that add up to $-12$ and multiply to $32$ The two numbers $-8$ and $-4$ satisfy both conditions: $ {-8} + {-4} = {-12} $ $ {-8} \times {-4} = {32} $ $(x {-8}) (x {-4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x -4) = 0$ $x - 8 = 0$ or $x - 4 = 0$ Thus, $x = 8$ and $x = 4$ are the solutions.